摘要
边坡可靠度计算最常用的三种方法有蒙特卡洛法(Monte Carlo Method)、点估计法(Rosenblueth Method)和可靠指标法(First-Order Second-momenet Method)。在坡型与参数确定的情况下,三种方法计算结果有一定的差异。目前边坡工程中还没有可靠度计算的统一标准,使用不同的计算方法对合理评价边坡可靠度存在困扰。针对这一问题,本文以黄土高边坡为研究对象,选用简化毕肖普法建立状态函数,通过变化强度参数、参数变异系数和坡型对三种可靠度计算方法所得结果进行了系统分析,结果认为：
(1)在稳定系数大于1.0的边坡中,蒙特卡洛所求失效概率大于点估计法和一次二阶矩法,最大差值达8%。而一次二阶矩法与点估计法所得结果相差较小。边坡稳定系数在1.3左右,蒙特卡洛法与其它两种方法计算结果相差最大,当边坡稳定系数大于1.5时,三种方法随稳定系数的增大失效概率降低幅度极小,说明理论上取安全系数为1.5更为合理。
(2)参数的均值控制着边坡的稳定系数,进一步控制着边坡失效概率和可靠指标,但参数的变异系数对失效概率的影响极大,随着δc和δφ的增大,蒙特卡洛法计算的失效概率与一次二阶矩法和点估计法计算得失效概率的差值增大,但并不是单调增加,达到峰值后,差值有所降低,这个峰值在δc=0.2～0.35之间和δφ=0.1～0.25之间；点估计法与一次二阶矩法的差值随δφ的增大；在单调增大。δc对蒙特卡洛法影响较大,对点估计法和一次二阶矩法影响较小。内摩擦角均值及变异系数δφ对三种计算方法的敏感性均高于粘聚力均值及变异系数δc。
(3)三种可靠度计算方法对坡高与坡率的变化敏感性较低,在稳定系数介于1～1.5之间时各种方法差值波动较小。在稳定系数增大时,蒙特卡洛法所得失效概率减小幅度小于点估计法和一次二阶矩法。
(4)综合强度参数、变异系数及坡型对三种方法所求结果差值的分析,提出用于公路边坡设计时,点估计法和一次二阶矩法的目标失效概率及可靠指标建议值。并推荐工程上采用点估计法进行可靠度计算。
Three common methods of calculating slope reliability are Monte Carlo Method, Rosenblueth Method and First-Order Second-momenet Method. In the case of slope style and its parameters having been decided, the results calculated by using these three methods have some specified difference. At present, slope projects have no uniform standard for reliability accounting. Using different measures can cause some specified obsession to reasonable evaluation of slope reliability. Aiming at solving this problem, the paper take high loess slope to be the object of study, choosing simplified Bishop Method to strike up state function and making systemic analysis on the result that variational intension parameter、coefficient of variation of the parameter and slope style bring to the three methods of calculating slope reliability, the conclusions are following as:
(1) In the slope whose stability coefficient is greater than 1.0, the disabled probability attained from Monte Carlo Method is greater than the ones from Rosenblueth Method and First-Order Second-momenet Method,the greatest difference can reach to 8%, yet, the disabled probability from First-Order Second-momenet Method has less difference with the one from Rosenblueth Method, when the stability coefficient comes about 1.3, the first difference is the greatest, with the stability coefficient increasing to a value which is greater than 1.5, the depressed extent of the increscent disabled probability is infinitesimal.
(2) The stability coefficient is under the control of the average value of parametric which fartherly controls the disabled probability and reliability index, however, the coefficient of variation of the parameter has great effect on the disabled probability, withδc andδφincreasing, the difference between the disabled probability obtained from Monte Carlo Method and the one from First-Order Second-momenet Method is growing, thus not monotonously growing, afterδc andδφarriving to the peak value, that is betweenδc=0.2-0.35 andδφ=0.1～0.25, the difference falls on the contrary, the difference between Rosenblueth Method and First-Order Second-momenet Method is monotonously growing withδφincreasing,δc has great effect on the Monte Carlo Method, thus little effect on the Rosenblueth Method and First-Order Second-momenet Method. The average angle of internal friction and the coefficient of variationδφhave more sensitivity on the three methods than the average adhesion and the coefficient of variationδc.
(3) This three methods of calculating reliability have lower sensitivity on the changement of slope height and slope ratio, the difference between these methods fluctuates less when the stability coefficient change between 1 and 1.5, as the stability coefficient increasing, the depressed extent of disabled probability received by Monte Carlo Method is smaller than by Rosenblueth Method and First-Order Second-momenet Method.
(4) Through synthesizing the analysis of the differences resulting from intensity parameter,coefficient of variation and slope style by using the three methods, this paper finally brings up object disabled probability and reliability index of Rosenblueth Method and First-Order Second-momenet Method in highway slope design. Therefore, it commends to use Rosenblueth Method to calculate reliability in the project.
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